The battle lines in the Wisconsin recall were supposed to be clear: Republican Gov. Scott Walker on one side, unions on the other, in a fight that would reorder the balance of power between government and organized labor.

Yet with less than two months until Election Day, the recall has turned into something more complicated — not just a war on Walker, but a debate within the Democratic coalition over exactly what the party’s message is going to be and how central a role labor issues ought to play.

It’s a struggle that’s playing out in the Democratic primary between Milwaukee Mayor Tom Barrett, who ran an unsuccessful race for governor in 2010 at the urging of the White House, and former Dane County Executive Kathleen Falk, the underdog who’s also the preferred candidate of the labor groups that led the charge against Walker’s labor agenda.

So far, the primary rhetoric between the candidates has been relatively tame, though there’s been some sniping from labor in Barrett’s direction.

But the subtext of the Democratic contest is real indecision over whether unions and their issues should be the primary focus of the recall fight, or whether this election should be treated like any other, with a less ideologically charged goal: winning.

“It is unfortunate that we’ve turned what was kind of a referendum on Scott Walker’s policies into a much more confused situation,” said Andy Stern, the former president of the national union SEIU. Stern bemoaned the attention being paid to “who’s the better labor candidate, who has the better chance of winning, and we are diluting the focus on I think what brought citizens to be so engaged with the sense of wanting to rebuild the right values of Wisconsin.”

“I’m not saying anyone’s at fault, but I think it completely complicates the situation and clearly dilutes what was a rather straightforward question for Wisconsin voters,” he said.

Stern said, and pretty much all sides of this labor debate agree, that defeating Walker in an epic symbolic contest is not the be-all, end-all for labor in Wisconsin — with a year’s worth of sprawling protests and state legislative battles, Walker’s opponents have already managed to sap his power.

Even if Walker escapes from the recall and hangs on to his job, union insiders say, they’ll still have sent the message to governors like him — and Ohio Gov. John Kasich, who lost a high-profile referendum on union issues last year — that they will pay a price for confronting labor.

“Our members are united and fighting back, and it’s inspired members across the country,” said Lee Saunders, secretary-treasurer of the public-sector labor giant AFSCME. “Recalling Walker is very important, but there’s already been a huge moral and psychological victory that doesn’t depend solely on recalling Walker. Labor is united and fighting for an economy (and a country) that works for and supports the 99 percent.”

What is at issue is a debate about political strategy that, depending on the primary’s outcome, could prevent unions from waging the straightforward grudge match they’d hoped for against the Republican.

If there’s an appetite in the labor community for explicitly making an example of Walker over collective bargaining, it’s not one that’s reflected in the messaging of national Democrats or the party’s leading gubernatorial candidate, Barrett.

Falk has collected endorsements from powerful labor groups such as the state-level branches of AFSCME and the AFL-CIO. Barrett earned a few local union endorsements this last week, but his most notable supporters are senior Democratic Party leaders: Sen. Herb Kohl, former Rep. David Obey and state Sen. Jon Erpenbach. Barrett has also taken a few slings and arrows from the House of Labor, as an AFSCME affiliate put out a web video, suggesting his views on unions are too close to the Republican incumbent’s views.

Far from calling for an ideological crusade against the governor, Maryland Gov. Martin O’Malley — chairman of the Democratic Governors Association — said his party would succeed if it could promise “a more balanced approach, a more practical approach” to governing Wisconsin.

“For the coalition of people that are hoping for a better Wisconsin and better days for Wisconsin, I think we have to move to that issue that unites everybody, and that is job creation,” said O’Malley, who is neutral in the Democratic primary. “I really think the key here, of getting beyond personalities and ideology is to focus on job creation.”

Labor issues are relevant, he said, but as part of a list of grievances against Republicans that include “actions that roll back women’s rights, roll back workers’ rights, roll back voting rights” and more.

Part of the Democratic desire to deliver a broader message in the recall campaign is a matter of practical politics: The Wisconsin electorate is extraordinarily polarized, strategists say, and it’s not clear that a “labor versus Walker” frame for the race will give the challenger a decisive edge.

One Republican operative familiar with polling on the race said the question of whether voters would prefer to close deficits through taxation or “spending cuts and reforms” is still “a winning issue” for Walker.

“People just don’t like the way [Walker] went about doing it,” said the strategist, who anticipates Barrett will be the Democratic nominee. “It’s going to be 52-48 one way or the other.”

On the other hand, Democrats say they recognize any overt inching away from unions would also be a mistake: In an agonizingly close race, a labor-driven ground game could make the difference.

In an interview with POLITICO shortly after announcing his campaign, Barrett said the collective-bargaining issue was important to the race — “I’m going to restore collective bargaining,” he said — but argued that the election is about more than that.

“I think there is a large set of issues, and I’m running to be governor of this entire state,” he said. “Cuts to education, the cuts to local government, the cuts to health care — those are important to me as well. But a big part of this is restoring trust to government.”

Falk has also taken steps to deliver a wider-spectrum message. Scot Ross, a spokesman for her campaign, said it would take a “big tent to defeat [Walker]” and cited a number of liberal coalition groups from which Falk has earned support: “Working men and women, environmentalists, women’s rights advocates, community organizers and young progressives.”

Asked if Falk accepted the label of being labor’s candidate in the race, Ross responded: “Kathleen is proud to stand up for the working men and women of Wisconsin and Kathleen has a record of delivering for working men and women.”

Still, there’s no question that labor has invested heavily in Falk — a union-backed group, Wisconsin for Falk, is spending about $534,000 on her behalf for April 12-17 alone.

By comparison, as of Friday, the Falk and Barrett campaigns had recorded less than $200,000 each in television buys since April 10.

All that spending is dwarfed by what Republicans are putting on the air: Walker’s campaign has reserved $1.2 million in TV ads for April 12-29, while the group Right Direction — backed by the Republican Governors Association — has already booked $2.6 million in airtime between now and Election Day. The primary is May 8; the general election is June 5.

Nick Everhart, a Republican media strategist who has worked in Wisconsin, called the pro-Falk effort a costly exercise in chest-thumping: “Labor’s ego and pride seems to be taking priority over smart political investments.”

“It’s definitely a situation where it’s going to test the limits of what grass-roots organization means in a post-Citizens United world,” said one Wisconsin source sympathetic to the campaign against Walker, echoing a refrain that many Democrats have used about outside spending in races so far this cycle.

Yet the anti-Walker group, We Are Wisconsin, is also making a play in three state Senate seats in which there are recall races, all of which are competitive — and winning just one would tilt the balance of power, making it difficult for Walker to get an agenda through, going forward. And labor officials insist discussions of a divide since Barrett entered the race are overblown and media-fueled.

Labor insiders, meanwhile, argued that Barrett wouldn’t benefit from the same fired-up electorate as Falk because he wasn’t as high-profile a player in protests against the governor last year. Voter enthusiasm will be critical in the recall fight, both because of the closeness of the race and the shortness of the campaign.

But the flip side for labor is that coming out strongly against Barrett could ultimately have the effect of hobbling Democrats in the general election — and upping the odds that Walker can claim vindication two months from now. Nationally, Republicans will tout a win as evidence that the throw-the-bums-out mentality of the 2010 electorate had staying power, and use it to fire up their base for the fall.

Billionaire David Koch, who Democrats have tried to turn into a symbol of outside spending dangers and special interests — and who has helped fund the pro-Walker side — put it bluntly to the Palm Beach Post in February: “If the unions win the recall, there will be no stopping union power.”

At the National Rifle Association convention in St. Louis Friday, the governor cast his campaign as an apocalyptic showdown with “the advocates for big government.”

“They want to take me out,” he said. “Lord, help us if somehow we fail. … It sets us back at least a decade, if not a generation.”

Stern wouldn’t go quite that far, but no one in the Democratic-labor coalition plays down the value of a win.

“I think the battle has been significantly won” by unions over the past year, Stern said. “But I think a victory here would put this issue to rest for a long time.”